How do you increase your chances of getting into a top class university?

For Oxbridge, your best bet will be to have stellar grades. That is typically the main criterion used when selecting people for interviews.
If you do get an invitation for an interview - congratulations. While you can’t be fully prepared for an Oxbridge interview, that’s also the charm of such interviews, because you are expected to not know things. Make sure you know what you’re supposed to know, and try reading up recent developments in your field of interest in the 2 weeks before your interview. Stay calm, so that your mind stays sharp to the puzzles that the interviewers are going to pose to you. They are assessing how fast you’re able to assimilate new information and use it to solve problems, and how receptive you are to learning new things.
For the admissions test, there is significant weightage as that’s the only standardised grading the uni has to discriminate students taking different exam qualifications. Make sure you practice for it, up to a month in advance.

Top class universities are looking for students who go above and beyond academic achievement. They want students who:
1) Are active members of their communities (for example, their school or local community)
2) Have developed teamwork and/or leadership qualities through extracurricular and sporting activities
3) Show curiosity and interest in current and global affairs
4) Actively seek out and embrace these opportunities
5) Demonstrate commitment to these activities alongside their academic studies (showing excellent time management skills and the ability to prioritise)
Good luck!